Mendeley出力
＜図書＞
Geometry and topology
| 責任表示 | Miles Reid, Balász Szendrői |
|---|---|
| データ種別 | 図書 |
| 出版情報 | Cambridge : Cambridge University Press , 2005 |
| 本文言語 | 英語 |
| 大きさ | xviii, 196 p. : ill ; 26 cm. |
| 概要 | Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. The book introduces the ideas of...geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the Mobius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups, having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. While the book requires minimal prerequisites, it provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics. Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. The book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the Mobius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups, having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. While the book requires minimal prerequisites, it provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics.続きを見る |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
|---|---|---|---|---|---|---|---|---|---|---|
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hbk. | 理系図3F 数理独自 | REID/30/3 | 2005 |
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023212005005741 |
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書誌詳細
| 一般注記 | Includes bibliographical references and index |
|---|---|
| 著者標目 | *Reid, Miles Szendrői, Balász |
| 件 名 | LCSH:Geometry LCSH:Topology |
| 分 類 | DC22:516 |
| 書誌ID | 1001242566 |
| ISBN | 052184889X |
| NCID | BA74339994 |
| 巻冊次 | : hbk ; ISBN:052184889X ; XISBN:9780821848893 : pbk ; ISBN:0521613256 ; XISBN:9780521613255 |
| NBN | GBA554519 |
| 登録日 | 2009.09.18 |
| 更新日 | 2009.11.02 |